Trigonometric Equations

Simplifying Trigonometric Equations

• Start by identifying what type of trigonometric equation it is, i.e., it may involve sine, cosine, or tangent.
• Note the range of the trigonometric function and corresponding values.

Solving Basic Trigonometric Equations

• You can solve base trigonometric equations like sin(x) = 0, cos(x) = 0, and tan(x) = 0 with special angles.
• For example, sin(x) = 0 implies x = nπ where n belongs to integer, that’s because the sine function is 0 at all multiples of π.

Solving Trigonometric Equations Involving Multiple Angles

• Trigonometric equations can involve multiple angles, so the key to solving them is to reduce the equation to a standard form.
• For example, if you have sin(2x) = 0, you can use the double angle identity (sin(2x) = 2sin(x)cos(x)) and then solve the equation as above.

Equations with Trigonometric Identities

• Always simplify the trigonometric equation (if possible) using identities, such as the Pythagorean identity (sin2(x) + cos2(x) = 1) or the double-angle identities.
• Convert the equation into terms of a single trigonometric function if possible, which makes it easier to solve.